Match the correct statement with the given information.
Column A
1.
A cone's radius increases x 3:
a
A cone's radius increases x 3
2.
A cone's height increases x 3:
h
A cone's height increases x 3
3.
A sphere's radius increases x 3:
g
A sphere's radius increases x 3
4.
A cylinder's radius increases x 6:
j
A cylinder's radius increases x 6
Column B
a.The cone's volume will increase x 9
b.The sphere's volume will increase x 3
c.The sphere's volume will increase x 6
d.The cylinder's volume will increase x 6
e.The cone's volume will increase x 6
f.The cylinders volume will increase x 36
g.The sphere's volume will increase x 27
h.The cone's volume will increase x 3
i.The cylinder's volume will increase x 18
j.The cylinder's volume will increase x 12
k.The sphere's volume will increase x 9
1. a - The cone's volume will increase x 9
2. h - The cone's volume will increase x 3
3. g - The sphere's volume will increase x 27
4. j - The cylinder's volume will increase x 12
To match the correct statement with the given information, we need to understand the formulas for calculating the volumes of different shapes.
1. A cone's radius increases x 3: This means that the new radius of the cone is three times the original radius.
2. A cone's height increases x 3: This means that the new height of the cone is three times the original height.
3. A sphere's radius increases x 3: This means that the new radius of the sphere is three times the original radius.
4. A cylinder's radius increases x 6: This means that the new radius of the cylinder is six times the original radius.
Now, let's look at the statements in Column B and find the correct matches.
a. The cone's volume will increase x 9: This statement matches with statement 1. When the cone's radius increases by a factor of 3, the volume increases by a factor of 9.
b. The sphere's volume will increase x 3: This statement matches with statement 3. When the sphere's radius increases by a factor of 3, the volume increases by a factor of 27 (3^3 = 27).
c. The sphere's volume will increase x 6: This statement does not have a match in Column A.
d. The cylinder's volume will increase x 6: This statement matches with statement 4. When the cylinder's radius increases by a factor of 6, the volume increases by a factor of 36 (6^2 = 36).
e. The cone's volume will increase x 6: This statement does not have a match in Column A.
f. The cylinder's volume will increase x 36: This statement does not have a match in Column A.
g. The sphere's volume will increase x 27: This statement matches with statement 3. When the sphere's radius increases by a factor of 3, the volume increases by a factor of 27 (3^3 = 27).
h. The cone's volume will increase x 3: This statement matches with statement 1. When the cone's radius increases by a factor of 3, the volume increases by a factor of 9.
i. The cylinder's volume will increase x 18: This statement does not have a match in Column A.
j. The cylinder's volume will increase x 12: This statement matches with statement 4. When the cylinder's radius increases by a factor of 6, the volume increases by a factor of 36 (6^2 = 36).
k. The sphere's volume will increase x 9: This statement matches with statement 3. When the sphere's radius increases by a factor of 3, the volume increases by a factor of 27 (3^3 = 27).
So, the correct matches would be:
1. a
2. h
3. g
4. j
Matching the correct statement with the given information:
1. A cone's radius increases x 3:
Column B - h. The cone's volume will increase x 3.
2. A cone's height increases x 3:
Column B - e. The cone's volume will increase x 6.
3. A sphere's radius increases x 3:
Column B - g. The sphere's volume will increase x 27.
4. A cylinder's radius increases x 6:
Column B - j. The cylinder's volume will increase x 12.